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New Mexico State University
College of Arts and Sciences
Department of Mathematical Sciences

Analysis Group

Faculty
Lolina Alvarez Harmonic and Functional Analysis: Function spaces, pseudo-differential operators, interplay between harmonic analysis and distribution theory.
Tiziana Giorgi Non-linearPartial Differential Equations: existence, uniqueness (up to a guage) and stability of minimizers to energy funtionals with applications to superconductivity.
Doug Kurtz Harmonic Analysis: maximal functions, singular integrals, multipliers, Littlewood-Paley operators, weighted norm inequalities.
Joe Lakey Harmonic Analysis: time-frequency analysis, wavelets, information theory and applications to signal processing, discrete dynamical systems.
Maria Cristina Mariani Nonlinear Partial Differential Equations:Nonlinear partial differential equations and Stochastic Differential Equations, mathematical finance, mathematical physics, functional analysis and statistical mechanics.
Robert Smits Stochastic and Harmonic Analysis: stochastic differential equations, spectral theory, asymptotic analysis, heat kernels, large deviations, mathematical finance, eigenvalue estimates.
Christopher Stuart Functional Analysis: uniform boundedness principles, barrelled spaces, the topological vector space properties of sequence spaces.
Caroline Sweezy Harmonic Analysis, Complex Analysis, Applications to Partial Differential Equations: weighted inequalities for parabolic and elliptic functions on nonsmooth domains, atomic spaces between H^1 and L^1, Carleson measure conditions, square functions and the exponential square class.
Emeritus Faculty
Dick Bagby Real and Harmonic Analysis: Classical analysis in Euclidean space. Convolution and Fourier multipliers. Continuity properties of operators and bounds for maximal functions in terms of function space norms. Questions of pointwise convergence.
Chuck Swartz Functional Analysis: topological vector spaces, infinite matrices and gliding hump properties in sequence and function spaces, vector and operator valued series, vector valued measures and integrals.

Group Activities:

With the support of the National Science Foundation, our group organizes the annual New Mexico Analysis Seminar jointly with analysts from the University of New Mexico.